Car A was traveling east at high speed when it collided at point O with car B, w

Question

Car A was traveling east at high speed when it collided at point O with car B, which was traveling north at 50 mi/h. Car C, which was traveling west at 65 mi/h, was 32 ft east and 10 ft north of point O at the time of the collision. Because the pavement was wet, the driver of car C could not prevent his car from sliding into the other two cars, and the three cars, stuck together, kept sliding until they hit the utility pole P. Knowing that the weights of cars A, B, and C are, respectively, 3000 lb, 2600 lb, and 2400 lb, and neglecting the forces exerted on the cars by the wet pavement, solve the problems indicated. Knowing that the speed of car A was 85 mi/h and that the time elapsed from the first collision to the stop at P was 2.4 s, determine the coordinates of the utility pole P (Round the final answer to two decimal places.) Up The coordinates of pole P are: Xp 206.81 ft yp 51.04ft Hints eBook & Resources Hint #1 References

Explanation / Answer

initial position of center of mass,

x0 = (0 + (32 x 2400))/ (3000 + 2600 + 2400)

x0 = 9.6 ft

y0 = (0 + (10 x 2400))/(3000 + 2600 + 2400)

y0 = 3 ft

vx = ((3000 x85) + (0)+(2400 x -65))/(3000 + 2400 + 2600)

vx = 12.375 mi/h = (12.375 x 5280 ft / 3600s)

vx = 18.15 ft /s

vy = ((0) + (2600 x 50) + (0))/(3000 + 2400 + 2600)

vy = 16.25 mi/h = 23.83 ft/s

t = 2.4 sec

x = x0 + (vx)(t) = 53.16 ft

y = y0 + (vy)(t) = 60.2 ft

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